We consider translational-rotational diffusion for spherical colloidal particles that carry a preferred body-fixed axis specified by a unit vector n. Using a Smoluchowski equation description we derive moment conditions for small increments in position, ΔR, and orientation, Δn, occuring in a time Δt, in the limit that Δt→0. We compare these with results derived by integration of Langevin equations and expressed in terms of rigid body rotations. We obtain Brownian dynamics update equations consistent with these moment conditions and expressible directly in terms of the position and orientation vectors, R and n. For a single particle diffusing near a hard wall in the presence of a wall potential and external torques we give numerical simulation results. The hydrodynamic interaction of particle and wall strongly inhibits both translational and rotational diffusion while coupling of translations and rotations is negligible.
